A spectrophotometer measures the reflectance of an illuminated object of interest over many wavelengths. Typically, a spectrophotometer uses 16 to 36 channels to cover the wavelengths between 380 nm to 780 nm, within the human visible spectral range. One example is the MEMS Fabry-Perot spectrophotometer as an array color sensor with tunable wavelengths as described in detail in U.S. Pat. No. 6,295,130, and U.S. patent application Ser. No. 11/535,382, filed Sep. 26, 2006, entitled “MEMS Fabry-Perot Inline Color Scanner For Printing Applications Using Stationary Membranes,” which are incorporated herein by reference.
FIG. 1 shows the basic structure of a Fabry-Perot spectrophotometer. The spectrophotometer 100 is preferably fabricated using semiconductor microelectromechanical system (MEMS) processing techniques with a photodetector 175, and a Fabry-Perot cavity filter 110 monolithically integrated on a substrate 185 that is typically silicon. Silicon wafer 190 is aligned over the silicon wafer 185 and the Fabry-Perot filter 110 using a flip-chip pick and drop aligner. Optical fiber 199 is inserted into a circular hole 195 and epoxied to silicon wafer 190.
The cavity filter 110 includes two micro-mirrors 120, 130 separated by a gap 125. The gap 125 may be an air gap, or may be filled with a liquid or other dielectric material. The micro-mirrors 120, 130 include multi-layer distributed Bragg reflector (DBR) stacks 115 of highly reflective metallic layers, such as gold. A voltage applied between the two mirrors across transparent electrodes 135, 140 may be adjusted to change a dimension d of a gap, such as a size of the gap. Only light incident normal to the micro-mirror with wavelengths near,λ=2nd/m with m=1,2,3 . . .  (1)will be able to pass the gap and reach the photodetector 175 due to interference effect of incident light and reflective light within the gap.
In Eq. (1), n represents the refractive index of the gap material (n=1 for air), and d is the gap distance.
Usually, a spectrophotometer is calibrated by measuring the spectra of a standard white tile with known reflectance. A scaling factor used to calibrate the sensor is given by
                              f          ⁡                      (            λ            )                          =                                            R              w                        ⁡                          (              λ              )                                                                          V                w                            ⁡                              (                λ                )                                      -                          D              ⁡                              (                λ                )                                                                        (        2        )            where Rw(λ) is the reflectance of the white tile, Vw(λ) is the sensor measurement for the white tile, and D(λ) is the dark reading of the sensor. The reflectance R(λ) of an arbitrary object with V(λ) as the unscaled measured reflectance by the sensor is given byR(λ)=[V(λ)−D(λ)]f(λ)  (3)
FIG. 2 shows the method used for the conventional white tile calibration procedure. Beginning at step 2000, the process continues to step 2001, where white tile measurements from the sensor Vw(λ) at each wavelength λ are obtained. The process then continues to step 2002 where the dark reading D(λ) of the sensor is measured. Continuing to step 2003, the scaling factor f(λ) is calculated according to Eq. (2).
In step 2004 measurements V(λ) of an arbitrary object at each wavelength λ are obtained using the sensor. Next, in step 2005 the reflectance R(λ) of the object is computed according to Eq. (3). Continuing to step 2006, a determination is made whether a further object is to be measured. If not, the process continues to step 2007. Otherwise, the process steps 2004, 2005 and 2006 may be repeated, as necessary, for a plurality of object measurements. Finally, the process ends in step 2007.
There are a few potential problems, however, that can cause inaccuracies with this calibration procedure. They are:
(1) The dark reading may not be accurate and is generally noisy due to low signal levels.
(2) The accuracy of the sensor measurement at a given wavelength may vary. For the example of the MEMS Fabry-Perot sensor, the accuracy depends on the uniformity of the gap between Fabry-Perot cavity reflectors. The deviation of the gap from the nominal value as given in Eq. (1) may also result in an inaccurate reading.
(3) Noise or deficiency in a part of the spectra of the light source may also introduce inaccuracy in the sensor output. For example, if the light source is deficient at the blue end, the measurements Vw(λ) and V(λ) in Eq. (2) and Eq. (3) may be equal to or even smaller than the dark reading D(λ) for the blue lights, creating the situation that the reflectance obtained from this calibration method becomes unreliable. This situation happens quite often in real practice. Better blue light sources, specifically blue LEDs, are now becoming available. However, such light sources may not always be available or may even be too expensive to instrument in a low cost sensor.
(4) Structural differences/variations during manufacture between multiple pixel elements can lead to pixel-to-pixel measurement variation.
Thus, there is a need for an improved calibration procedure to further improve the sensor accuracy performance in the presence of these problems and many unknown structural and procedural defects in color sensor.